| KU Interactive Mathematics |
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Here, we present a definition of the transcendental number e using a table.
| What to Enter | Screen Shots |
| The e can be defined as the limit of (1 + 1/x)x as x → ∞. |  |
| The graph of y = (1 + 1/x)x is seen here: |  |
| But, we are interested only in the part that corresponds to x > 0. So, we will change the window dimensions and GRAPH again. |  |
| Then, we will get a better graph. It raises our curiosity as to how quickly the graph gets almost flat. That is why we want to evaluate (1 + 1/x)x at various values of x. By the graph, we conjecture that the values of (1 + 1/x)x approach 2.5 as x gets larger. One way to find out is to perform actual computations. |
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| Press 2ND then TBLSET (above WINDOW). Then, you will see this: |  |
| Note that (1 + 1/x)x is not defined at x = 0. So, we set TblStart=1. Next, ΔTb1 defines the increment for the independent variable. For the moment, set ΔTb1=10. |
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| Press 2ND then TABLE (above GRAPH). Then, you will see this: |  |
| Increase ΔTb1=1000. Then, you will get this: |  |
| Increase ΔTb1=10000. Then, you will get this: It appears that the values of (1 + 1/x)x are approaching 2.7183. |
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| Press 2ND then QUIT to get a blank screen. Then, press 2ND then ex (above LN) to get the natural exponential function, and evaluate it at 1. What is now on display coincides with what we got from the table. The e is a non-terminating non-repeating decimal. |
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| KU Interactive Mathematics |
Disclaimer • Updated September 4, 2008
Email: mitsuma@kutztown.edu
Phone: +1 (610) 462-WPJW
Phone: +1 (610) 462-WPJW